College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.5 - Factoring Polynomials - R.5 Assess Your Understanding: 77

Answer

number to be added: $\dfrac{1}{16}$ factored form: $(x-\frac{1}{4})^2$

Work Step by Step

RECALL: To complete the square of an expression in the form $x^2-bx$, $(\frac{b}{a})^2$ must be added. The factored form of the result is $(x-\frac{b}{2})^2$. Thus, in the given expression add $(\dfrac{\frac{1}{2}}{2})^2=(\frac{1}{4})^2=\frac{1}{16}$ to obtain: $x^2 -\frac{1}{2}x + \frac{1}{16}$ Writing the square in factored form gives: $x^2-\frac{1}{4}x+\frac{1}{16} = (x-\frac{1}{4})^2$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.